This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A361576 #15 Aug 01 2025 18:51:59
%S A361576 1,0,0,0,24,480,7200,100800,1431360,21772800,370137600,7185024000,
%T A361576 158150361600,3848298854400,100865282918400,2799294930432000,
%U A361576 81599752346112000,2492894621048832000,79852538982408192000,2684220785621286912000
%N A361576 Expansion of e.g.f. exp((x / (1-x))^4).
%F A361576 E.g.f.: exp( (x / (1-x))^4 ).
%F A361576 a(n) = n! * Sum_{k=0..floor(n/4)} binomial(n-1,n-4*k)/k!.
%F A361576 a(0) = 1; a(n) = (n-1)! * Sum_{k=4..n} (-1)^(k-4) * k * binomial(-4,k-4) * a(n-k)/(n-k)!.
%F A361576 a(n) = 5*(n-1)*a(n-1) - 10*(n-2)*(n-1)*a(n-2) + 10*(n-3)*(n-2)*(n-1)*a(n-3) - (n-3)*(n-2)*(n-1)*(5*n - 24)*a(n-4) + (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5). - _Vaclav Kotesovec_, Mar 17 2023
%t A361576 Table[n! * Sum[Binomial[n-1,n-4*k]/k!, {k,0,n/4}], {n,0,20}] (* _Vaclav Kotesovec_, Mar 17 2023 *)
%t A361576 With[{nn=20},CoefficientList[Series[Exp[(x/(1-x))^4],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 01 2025 *)
%o A361576 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((x/(1-x))^4)))
%o A361576 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=4, i, (-1)^(j-4)*j*binomial(-4, j-4)*v[i-j+1]/(i-j)!)); v;
%Y A361576 Cf. A000262, A052887, A361572.
%K A361576 nonn
%O A361576 0,5
%A A361576 _Seiichi Manyama_, Mar 16 2023